Spearman's rank correlation coefficient

Understanding Spearman’s Rank Correlation Coefficient

• Spearman’s rank correlation coefficient, also known as Spearman’s rho, is a measure of the strength and direction of the relationship between two ranked variables.
• It’s a nonparametric test, which means it can be used when data is not normally distributed.
• It refers to the degree of association between the two variables, and it can vary between -1 to +1.

Calculating Spearman’s Rank Correlation Coefficient

• Spearman’s rank correlation coefficient is calculated using ranked values for both variables.
• First, rank the values of each variable independently, with 1 given to the highest score.
• Then, find the difference in ranks (d) for each pair of values.
• Square these differences (d²) and sum them (∑d²).
• Spearman’s rank correlation coefficient (rs) is then calculated using the formula 1 - (6∑d²/(n(n²-1))), where n is the number of pairs.

Interpretation of Spearman’s Rank Correlation Coefficient

• The sign of Spearman’s rho indicates the direction of the relationship. A positive correlation coefficient indicates that as one variable increases, the other also increases (direct correlation). A negative coefficient means that as one variable increases, the other decreases (inverse correlation).
• The magnitude of the coefficient indicates the strength of the relationship. A coefficient close to +1 or -1 shows a strong relationship, while a coefficient near 0 shows a weak relationship.

Assumptions for Spearman’s Rank Correlation Coefficient

• Both variables should be ordinal, which means they can be categorised and have a logical order.
• The relationship between the variables should be monotonic. The ranks should either continuously increase or decrease together.
• There should be no tied ranks. If there are tied ranks, a corrected formula for Spearman’s rho should be used.

Limitations of Spearman’s Rank Correlation Coefficient

• Spearman’s rank correlation coefficient cannot identify a curvilinear relationship; it only determines monotonic relationships.
• It’s sensitive to outliers, which can greatly influence the correlation coefficient.
• It does not provide information about the slope or intercept of the relationship between the variables. It only gives information about the strength and direction of the correlation.

Using Spearman’s Rank Correlation Coefficient

• It can be used in fields like psychology, business, and medicine, where it is often necessary to determine the relationship between non-parametric or ranked variables.
• It’s often preferred over Pearson’s correlation coefficient when the data are ordinal and does not meet the assumptions of the parametric test.